Question: A circle has a sector with area $20\pi$ and central angle $\dfrac{2}{5}\pi$ radian. What is the area of the circle? {100\pi} \color{#9D38BD}{\dfrac{2}{5}\pi} {20\pi}
Explanation: The ratio between the sector's central angle $\theta$ and $2 \pi$ radians is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{2 \pi} = \dfrac{A_s}{A_c}$ $\dfrac{2}{5}\pi \div 2 \pi = 20\pi \div A_c$ $\dfrac{1}{5} = 20\pi \div A_c$ $A_c \times \dfrac{1}{5} = 20\pi$ $A_c = 20\pi \times 5$ $A_c = 100\pi$